Hybrid modeling integrates machine learning with scientific knowledge with
the goal of enhancing interpretability, generalization, and adherence to
natural laws. Nevertheless, equifinality and regularization biases pose
challenges in hybrid modeling to achieve these purposes. This paper introduces
a novel approach to estimating hybrid models via a causal inference framework,
specifically employing Double Machine Learning (DML) to estimate causal
effects. We showcase its use for the Earth sciences on two problems related to
carbon dioxide fluxes. In the $Q_{10}$ model, we demonstrate that DML-based
hybrid modeling is superior in estimating causal parameters over end-to-end
deep neural network (DNN) approaches, proving efficiency, robustness to bias
from regularization methods, and circumventing equifinality. Our approach,
applied to carbon flux partitioning, exhibits flexibility in accommodating
heterogeneous causal effects. The study emphasizes the necessity of explicitly
defining causal graphs and relationships, advocating for this as a general best
practice. We encourage the continued exploration of causality in hybrid models
for more interpretable and trustworthy results in knowledge-guided machine
learning.

通过因果推断框架运用 Double Machine Learning（DML）估计混合模型，展示了在地球科学领域中估计因果参数的优势、对正则化方法偏差的鲁棒性以及避免等效多样性。该方法在碳通量配分中展现了适应异质因果效果的灵活性，并强调了明确定义因果图和关系的必要性，提倡这作为一般最佳实践，鼓励继续探索混合模型中的因果性以获得更可解释和可信赖的知识导向机器学习结果。